This paper deals with the performance enhancement for crystallization unit of a sugar plant using genetic algorithm. The crystallization unit of a sugar industry has three main subsystems arranged in series. Considering exponential distribution for the probable failures and repairs, the mathematical formulation of the problem is done using probabilistic approach, and different...

Amathematical model is developed with a highly controlled birth and death process for precursor cells. This model is both biologically- and statistically-based. The controlled growth and differentiation (CGD) model limits the number of replications allowed in the development of a tissue or organ and thus, more closely reflects the presence of a true stem cell population. Leroux et al. (1996) pr...

Methods for fitting nonhomogeneous Markov models to panel-observed data using direct numerical solution to the Kolmogorov Forward equations are developed. Nonhomogeneous Markov models occur most commonly when baseline transition intensities depend on calendar time, but may also occur with deterministic time-dependent covariates such as age. We propose transition intensities based on B-splines a...

It is known that if a stochastic process is a solution to a classical Itô stochastic differential equation (SDE), then its transition probabilities satisfy in the weak sense the associated Cauchy problem for the forward Kolmogorov equation. The forward Kolmogorov equation is a parabolic partial differential equation with coefficients determined by the corresponding SDE. Stochastic processes whi...

Abstract. We develop a new method to uniquely solve a large class of heat equations, so called Kolmogorov equations in infinitely many variables. The equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper (Lyapunov type) functions. This way for the first time the solutions are constructed everywhere without exceptional sets for equations with possibly no...

A problem of analyzing Markov systems along with a large number states has been considered. The conventional computational procedure for obtaining analytical ratios calculating the distribution system is based on use Kolmogorov differential equations. linear algebraic equations being formed later can be easily solved numerically. However, complexity an solution increases rapidly increase in dim...

Motivated by the probabilistic methods for nonlinear differential equations introduced McKean (1975) Kolmogorov-Petrovski-Piskunov (KPP) equation, and Le Jan Sznitman (1997) incompressible Navier-Stokes equations, we identify a new class of stochastic cascade models, referred to as Doubly Stochastic Yule cascades. We establish non-explosion criteria under assumption that randomization intensiti...

We apply the method of differential inequalities for computation upper bounds rate convergence to limiting regime one specific class (in)homogeneous continuous-time Markov chains. Such an approach seems very general; corresponding description and were considered earlier finite chains with analytical in time intensity functions. Now we generalize this locally integrable Special attention is paid...

In the literature, several numerical methods are proposed for solvingnth-order fuzzy linear differential equations. However, till now there areonly two analytical methods for the same. In this paper, the fuzzy Kolmogorov'sdifferential equations, obtained with the help of fuzzy Markov modelof piston manufacturing system, are solved by one of these analytical methodsand illustrated that the obtai...